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An Efficient Iterative Method for Reconstructing Surface from Point Clouds

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Abstract

Surface reconstruction from point clouds is a fundamental step in many applications in computer vision. In this paper, we develop an efficient iterative method on a variational model for the surface reconstruction from point clouds. The surface is implicitly represented by indicator functions and the energy functional is then approximated based on such representations using heat kernel convolutions. We then develop a novel iterative method to minimize the approximate energy and prove the energy decaying property during each iteration. Asymptotic expansion is also performed to illustrate the dynamics of the surface during iterations. Extensive numerical experiments are performed in both 2- and 3- dimensional Euclidean spaces to show that the proposed method is simple, efficient, and accurate.

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Data Availability

The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.

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Acknowledgements

This work is partially supported by the University Development Fund from The Chinese University of Hong Kong, Shenzhen (UDF01001803). D. Wang would like to thank Wei Hu, Hao Liu, and Jun Ma for helpful discussions and Xiao-Ping Wang for constant support, help and encouragement.

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  1. School of Science and Engineering, The Chinese University of Hong Kong, Shenzhen, 518172, Guangdong, People’s Republic of China

    Dong Wang

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Wang, D. An Efficient Iterative Method for Reconstructing Surface from Point Clouds. J Sci Comput 87, 38 (2021). https://doi.org/10.1007/s10915-021-01457-4

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